Math 220 Assignment

November 2, 2001

Due Monday, November 5

  1. What is the length of the line segment from the point (2, -1, 1) to the point (4, -4, 7) ?

  2. What is the angle at the point (0, 1, -1) in the triangle whose vertices are that point, the point (-1, 3, 1), and the point (3, 7, -3) ?

  3. Let M be the 2 \times 3 matrix

     M  =  
    (
    0
    -1
    3
    -2
    0
    )
      , 
    and let f be the linear function from R^{3} to R^{2} that is defined by f(x) = M x. Find a basis of the kernel of f consisting of vectors of length 1.
  4. Find a basis consisting of mutually perpendicular vectors for the plane in R^{3} defined by the linear equation

     2 x - y + 2 z  =  0  .  

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